Is it possible to separately evolve a part of the population?
There have been extensive studies within evolutionary computation in the area of island models and niching for doing exactly this.
The advantages of this approach include greater population diversity (which is particularly useful when the problem is multiobjective) and the potential for concurrent execution of each separate population.
See also the answers to the question What is the niching scheme?.
With specific reference to genetic programming, here is a recent paper that uses a parallel island model.